Waveform design course Chapters 7 & 8 from Waveform Design for Active Sensing Systems A computational approach

Cross ambiguity function (CAF) CAF has more degrees of freedom compared to that of the conventional ambiguity function, a case where v(t) equals u(t).

Discrete-CAF synthesis Under the assumptions that It can be proved that

Design problem

Cyclic algorithm (CA) for discrete-CAF synthesis Using the following notations

CA contd.. C2 can be re-written as

CA steps

Discrete CAF with weights

Numerical examples

Numerical examples

Numerical examples

Numerical examples

Numerical examples

Continuous time CAF synthesis

Continuous time CAF synthesis

CA for CAF synthesis

Numerical example

Numerical example

Joint design of transmit sequence and receive filter In Radars/Sonars. Conventional receiver : Matched filter (MF) (in the case of Doppler shifts, a bank of filters). MF maximizes the signal-to-noise ratio (SNR). Apart from noise here one can also have clutters. Signal to clutter-plus interference ratio (SCIR)

Data model and problem formulation

MSE of the mis-matched filter

CREW (gra) Minimization of MSE wrt to w Concentrated MSE : Minimization problem : which can be tackled via gradient methods like BFGS (Broyden-Fletcher-Goldfarb-Shanno) method – requires only gradient.

A frequency domain approach

Contd.. Using the circulant parameterization

Contd.. Using the DFT matrices to diagonalize the circulant matrices

CREW (fre) The design problem can be re-written as Minimizer over {hp} Minimization over {εp}

CREW (fre) Minimization over {zp} is convex, it can be solved using the Lagrangian methods Using Lagrangian multipliers

CREW (fre) Once {|εp|} is obtained, x can be obtained via which can be solved by a CA, unimodular and PAR constraints can be imposed.

Lower bound on MSE

CREW (mat) MSE for the matched filter Minimization over {εp}

Numerical examples

Jamming scenarios

Numerical example

Barrage jamming

Robust design

Robust design